Behringer's rep stems from quite a few products that had cold solder joints a few years back and they did not hold up on the road. I remember people swearing Behringer gear off. They also have taken to producing a large number of very obvious copy-cat products in the past couple of years, and apparantly they lost a suit brought by Roland in the case of some effects pedals. This all gave them a sleezy rep. Personally I've owned and used Behringer EQ's, effects and I currently use one of their mixers today - none of them have ever given me cause to complain but I use it in my studio and not on the road because of what I heard.
Peavey is generally the entry-level gear for lots of starting musos and churches. It's solid stuff and it works. I can't remember any of it failing either for me personally (long ago) or for my customers when I worked at a music store. JBL speakers just sound sooo much better but we already knew that.
The problem with both Peavey and Behringer is that there's very few MI stores I've been to that don't carry their stuff and it's in all the online stores/catalogs, which means you'll be lo-balled to death on price. But if you want to sell gear to the masses then it's probably the stuff to go with.